Method for determining the envelope curve of a modulated signal

ABSTRACT

The invention relates to a method for determining the envelope curve of a modulated input signal ( 5 ) with the following method steps: 
         generation of digital samples (A n ) by digital sampling ( 1 ) of the input signal ( 5 ),    generation of Fourier-transformed samples (B n ) by Fourier transformation of the digital samples (A n ),    generation of sideband-cleaned, Fourier-transformed samples (B′ n ) by removing the range with negative frequencies or the range with positive frequencies from the Fourier-transformed samples (B n ),    generation of inverse-transformed samples (C n ) by inverse Fourier transformation ( 4 ) of the sideband-cleaned, Fourier-transformed samples (B′ n ) and    formation of the absolute value of the inverse-transformed samples (C n ).

The invention relates to a method for determining the envelope curve ofa modulated signal, for example for determination of the values for aCCDF diagram.

The determination of the envelope curve of a modulated signal isrequired in particular for determination of the CCDF (ComplementaryCumulative Distribution Function) but also for other applications. TheCCDF diagram indicates the probability that the signal level of theenvelope curve of the analysed signal exceeds a specific level value.From the course of the CCDF diagram, the parameter of the crest factorinter alia can be determined, which parameter indicates the ratio of thepower occurring at the maximum in the signal relative to the averagepower. The crest factor assists the operator of a modulated highfrequency transmitter to determine the optimal modulation of thetransmitter amplifiers. On the one hand, the transmitted power isintended to be as high as possible in order that the signal-to-noiseratio at the receivers is as large as possible. On the other hand, thetransmitting power must not be too large in order to avoid destructiondue to short power peaks in the transmission amplifiers. If the measuredCCDF course together with the course of an ideal signal is represented,conclusions can be made with respect to non-linearity and limitationeffects in the transmitted signal.

A measurement value detecting device and display device for a CCDFdiagram is known from DE 199 10 902 A1. There also, a step of signalprocessing resides in determining the envelope curve of the modulatedsignal or the power of the envelope curve. In column 10, line -47 tocolumn 11, line 28, it is proposed for determining the envelope curvepower to sample the signal with the quadruple symbol frequency, tosquare the digital values of a group comprising four samples, to summateand then to divide by 4. Hence, a sliding average value of the powervalues of the instantaneous amplitude of the modulated signal isproduced, which corresponds to a low-pass filtering. It is howeverdisadvantageous in this mode of operation that the thereby necessarysquaring of the sampled digital values leads to higher-frequencyspectral components. The subsequent non-ideal low-pass filtering leadsto imprecisions in the CCDF measurement. More precisely, the squaring ofthe samples leads to higher-frequency spectral components which are nolonger removed correctly by means of averaging (=filtering with a filterwith sin(x)/x frequency response).

The object therefore underlying the invention is to indicate a methodfor determining the envelope curve of a modulated signal which operateswith relatively high precision.

The object is achieved by the features of claim 1.

In contrast to the known method, determination of the envelope curve iseffected according to the invention not by low-pass filtering butinstead the digital samples are Fourier-transformed in the frequencyrange. In the frequency range, the range of positive frequencies or therange of negative frequencies is then removed. Then a Fourier inversetransform in the time domain follows. Only then are the values of theinverse-transformed samples formed. It is also shown later in thisapplication that the absolute value of the inverse-transformed samplesrepresents the envelope curve of the modulated high frequency signal.

In contrast to the value formation and subsequent low-pass filtering,the method according to the invention has the advantage thatimplementation of the method is independent of the quality of thelow-pass filtering, is independent of the type of signal and of itsspectral position, and in addition independent of the synchronisationstate of the high frequency signal to be measured. The method accordingto the invention is in addition substantially more precise than theknown method with low-pass filtering.

The sub-claims relate to advantageous developments of the invention.

It is advantageous, in addition to the range of negative or positivefrequencies, also to remove the level component at the DC frequency 0after the Fourier transform in the frequency range. It is ensured as aresult that the direct voltage offset of a non-ideal analogue/digitalconverter has no influence on the method according to the invention. Theideal signal has no direct voltage component in the intermediatefrequency plane so that removal of the direct voltage component does notfalsify the measurement result.

Furthermore, it is sensible to further process the samples, which areinverse-transformed in the time domain, only in such a limited rangethat the cyclic continuation of the signal, which is caused by theFourier transform and inverse Fourier transform, is suppressed.

Claims 6, 7, 8 and 9 relate to a corresponding digital storage medium,computer programme or computer programme product based on the methodaccording to the invention.

The invention is described in more detail subsequently with reference tothe drawing. There are shown in the drawing:

FIG. 1 an example of a CCDF diagram; FIG. 2 a block diagram of themethod according to the invention;

FIG. 3 a diagram to explain the mode of operation of the methodaccording to the invention;

FIG. 4 the samples which are Fourier-transformed in the frequency rangeand

FIG. 5 the samples which are inverse-transformed in the time domain.

The method according to the invention is explained subsequently for theapplication example for determining the instantaneous power of theenvelope curve for a CCDF diagram. As already explained, the methodaccording to the invention is however not restricted to this applicationand is suitable for all applications in which the instantaneous level ofthe envelope curve or signal values derived from the latter, such ase.g. the power, i.e. the square of the level, are required.

FIG. 2 demonstrates the method according to the invention by means of ablock diagram. The high-frequency input signal S, which is modulated bya modulation signal, is firstly sampled digitally on a sampling andholding circuit 1. Digital samples A_(n) of the input signal S arethereby produced. The samples A_(n) are then subjected to a Fouriertransform for example with an algorithm of the fast Fourier transform(FFT, Fast Fourier Transform). The Fourier-transformed samples B_(n) areproduced as a result. The Fourier transform is illustrated in FIG. 2 byblock 2.

Due to the Fourier transform of a sampled real signal,Fourier-transformed samples are produced as is known, which samplesextend both over the range of negative frequencies and over the range ofpositive frequencies. According to the invention, either the range ofnegative frequencies or the range of positive frequencies is removedfrom the Fourier-transformed samples B_(n). If the index n is running,which indexes the Fourier-transformed samples B_(n), for example from−2^(N)/2 to 2^(N)/2−1, N being a whole natural number, then the range ofnegative frequencies corresponds to the samples B_(n) with n<0 or therange of positive frequencies corresponds to the samples B_(n) with n>0.

The remaining samples, which are either only positive or only negative,are designated in FIG. 2 with B′_(n). Trimming of the samples in thenegative frequency range is illustrated in FIG. 2 by the block 3 whichhas a transfer function H(f) which is different from 0 only in the rangeof positive frequencies. These sideband-cleaned, Fourier-transformedsamples B′_(n) are subsequently transformed back in the time domain byan inverse Fourier transform. Likewise, a fast digital Fourier inversetransform (IFFT, Inverse Fast Fourier Transform) can be used, which isillustrated in FIG. 2 by block 4. In the time domain, theinverse-transformed samples C_(n) are present, the value of which isstill to be formed finally in the value former 5. The value of thesamples, which are inverse-transformed in the time domain, is designatedin FIG. 2 with D_(m).

In the case of application of the CCDF diagram, there must now beestablished in a block 6 the relative frequency with which the square ofthe value-samples D² _(m), which corresponds to the power, exceeds athreshold value x in relation to the average power D² _(eff) on alogarithmic scale which is scaled in dB. Expediently, the squaring isimplemented not before but after logarithmising, i.e. instead of amultiplication by the factor 10, a multiplication by the scaling factor20 is effected: $\begin{matrix}{{{10 \cdot \log}\quad\frac{D_{m}^{2}}{D_{eff}^{2}}} = {{10 \cdot {\log( \frac{D_{m}}{D_{eff}} )}^{2}} = {{20 \cdot \log}\quad\frac{D_{m}}{D_{eff}}}}} & (1)\end{matrix}$

The CCDF diagram can then be displayed on a display device 7, forexample a screen.

As FIG. 5 shows, the signal, which is initially Fourier-transformed andthen inverse-transformed in the time domain, said signal comprising thedigital samples C_(n), is cyclic due to the final time and frequencysampling, i.e. in the example illustrated in FIG. 5, the signal has acycle length m₂-m₁−1. The index n runs in FIG. 5 from 0 to 2^(N)−1. Itis therefore expedient to further process the inverse-transformedsamples C_(n) only in a limited range 13 so that the cyclic continuationis suppressed, i.e. there applies C_(m)=C_(n) with m₁≦m≦m₂. The amountvalue is calculated only from this limited section C_(m) of theinverse-transformed samples, which corresponds to the description inFIG. 2. The value formation is then effected according to the formulaD _(m) =|C _(m) |=√{square root over (Re{C _(m) { ² +Im{C _(m) } ²)}  (2)

The steps for determining the values of the inverse-transformed samplesD_(m) are repeated until a sufficient number of values D_(m) isavailable such that the effective value D_(eff) of the value sequencecan be determined therefrom according to known rules. The power of thiseffective value is then the reference value for the indication of thelevel on the horizontal axis of the CCDF diagram (0 dB). On the verticalaxis of the CCDF diagram, the CCDF value, which belongs to therespective power level, is plotted, i.e. that relative frequency withwhich the power value x relative to the average power D² _(eff) isexceeded. This is effected by means of the formula $\begin{matrix}{{{CCDF}(x)} = {{p{( {{{20 \cdot \log_{\quad 10}}\frac{D}{\quad D_{\quad{eff}}}} \geq x} )\lbrack x\rbrack}} = {dB}}} & (3)\end{matrix}$with

-   -   p: probability of occurrence or relative frequency    -   D: instantaneous value of the envelope curve    -   D_(eff): effective value of the envelope curve

Instead, as here, of comparing level dimensions or voltage dimensions,of course also the corresponding power dimensions (instantaneous powerD² and average power D_(eff) ²) are related directly to each other. Thenthe pre-factor of the logarithm does however change from 20 to 10.

The function of the method according to the invention is described inmore detail with reference to FIGS. 3 and 4. The signal S can befactorised in a Fourier sequence, i.e. any arbitrary input signal can beconstructed from a series of cosine signals with different signal levelsand phases. In the following, only one of these Fourier components isconsidered, which can be written in general as follows:s ₁(t)=A(t) cos (ωt+φ)   (4)

The envelope curve to be determined here would therefore be A(t). Thetransmission signal concerns a real signal which can be representedcomplexly as follows: $\begin{matrix}\begin{matrix}{{s_{1}(t)} = {{A(t)} \cdot \lbrack {\frac{1}{2} \cdot ( {{\mathbb{e}}^{j \cdot {({{\omega \cdot \quad t} + \varphi})}} + {\mathbb{e}}^{{- j} \cdot {({{\omega \cdot t}\quad + \varphi})}}} )} \rbrack}} \\{= {{\frac{A(t)}{2} \cdot {\mathbb{e}}^{j \cdot {({{\omega \cdot \quad t} + \varphi})}}} + {\frac{A(t)}{2}{\mathbb{e}}^{{- j} \cdot {({{\omega \cdot t} + \varphi})}}}}}\end{matrix} & (5)\end{matrix}$

This relation can be presented graphically by means of a vector diagram,as illustrated in FIG. 3.

The signal s₁ (t) comprises a first rotating vector 8, which rotates tothe left with the angle frequency ω, and a second rotating vector 9synchronised thereto which rotates to the right with the same circularfrequency ω. The omission of the range of negative frequencies accordingto the invention leads to the fact that the rotating vector 9 issuppressed. In reverse, omission of the range of positive frequencies,which is just as possible as an alternative, leads to the fact that therotating vector 8 is suppressed. Filtering in the frequency range leadstherefore to omission of one of the two terms in equation (5). If forexample the component with the negative frequency, i.e. the rotatingvector 9 which rotates to the left in FIG. 3, is omitted in equation(4), then the following result is produced after the amount formation:$\begin{matrix}{{s_{2}(t)} = {{{\frac{A(t)}{2} \cdot {\mathbb{e}}^{+ {j{({{\omega \cdot \quad t} + \varphi})}}}}} = {{{\frac{A(t)}{2} \cdot {\mathbb{e}}^{- {j{({{\omega \cdot \quad t} + \varphi})}}}}} = \frac{{A(t)}}{2}}}} & (6)\end{matrix}$

The value corresponds according to FIG. 3 to the length of the remainingvector. When using the signal s₂ (t) for determining the CCDF diagram,the fact that s₂ (t) can only be positive because of the valueformation, is of no importance. In the case of the CCDF diagram, powersare compared with each other which can only be positive. The division bythe factor 2 does not likewise influence the result of the CCDF diagram.

The knowledge obtained above by means of a Fourier component can ofcourse be applied readily to the total signal which represents a linearsuperposition of a multiplicity of Fourier components. For this purpose,the Fourier-transformed samples B_(n) are represented in FIG. 4. Theindex n runs here from −2^(N)/2 to 2^(N)/2−1. It is detectable that therange of negative frequencies 10, in the case of a real input signal S,is the mirror. image of the range 11 with positive frequencies.

If either the range 10 of negative frequencies is omitted in the furthersignal processing, i.e.

-   B′_(n)=0 for n<0 and-   B′_(n)=B_(n) for n>0    or if the region 11 of positive frequencies is omitted, i.e.-   B′_(n)=B′_(n) for n<0 and-   B′_(n)=0 for n>0,    then the envelope curve is automatically produced after inverse    transformation in the time domain after formation of the absolute    value, as was illustrated previously with reference to FIG. 3.

Expediently, not only either the range 10 of negative frequencies or therange 11 of positive frequencies is suppressed, but in addition also thelevel component 12 for the zero frequency; in the indexation used here,i.e. B₀ with n=0. Thus a possibly present direct voltage component(DC-offset) is suppressed. Since the evaluated signals stem from theintermediate frequency plane, these should actually contain no directvoltage component. If however a direct voltage component is present,then this stems for example from a direct voltage offset of theanalogue-digital converter and removal of this direct voltage componentincreases the measurement precision.

An example of a CCDF diagram, the underlying envelope curve of which wasobtained with the method according to the invention, is illustrated inFIG. 1. As already mentioned, the relative frequency p is plotted forthis purpose in a CCDF diagram such that a specific level D on alogarithmic scale is exceeded. In the example illustrated in FIG. 3 ofan input signal which has been modulated digitally according to the 8VSBstandard, exceeding the effective power with 3 dB occurs still with arelative frequency of approximately 10%, whilst exceeding the effectivepower with more than 6 dB occurs already with a relative frequencysignificantly smaller than 1%.

As already mentioned many times, the method according to the inventionis not restricted to the application case for determining instantaneouslevel values or instantaneous power values for a CCDF diagram, but ingeneral is suitable for determining the envelope curve of a modulatedsignal. The method can be implemented both with digital hardware, forexample by using FPGA (Free Programmable Gate Array), or with softwarein a special processor, ideally in a digital signal processor (DSSP).

1. Method for determining the envelope curve of a modulated inputsignal, comprising the steps of: generating digital samples by digitalsampling a modulated input signal, generating Fourier-transformedsamples by Fourier transforming the digital samples, generatingsideband-cleaned, Fourier-transformed samples by removing a range withnegative frequencies or a range with positive frequencies from theFourier-transformed samples, generating inverse-transformed samples byinverse Fourier transforming the sideband-cleaned, Fourier-transformedsamples and forming values of the absolute value of theinverse-transformed samples.
 2. Method according to claim 1, comprisingremoving a level component at a zero frequency in addition to the rangewith the negative or positive frequencies in order to generate thesideband-cleaned, Fourier-transformed samples.
 3. Method according toclaim 1 , comprising processing the inverse-transformed samples furtheronly in such a limited range that a cyclic continuation, which is causedby the Fourier transform and inverse Fourier transform, is suppressed.4. Method according to claim 1, comprising logarithmizing the values ofthe absolute value relative to an effective value of theinverse-transformed samples.
 5. Method according to claim 4, comprisingdisplaying the frequency distribution of the logarithmized values as afunction of the logarithmized level complementary cumulativedistribution function diagram.
 6. Digital storage medium withelectronically readable control signals which can cooperate with aprogrammable computer or digital signal processor to implement themethod according to claim
 1. 7. Computer program product with a programcode stored on a machine-readable carrier in order to implement all thesteps according to claim 1 when the program is run on a computer or adigital signal processor.
 8. Computer program with program code in orderto implement all the steps according to claim 1 when the program is runon a computer or a digital signal processor.
 9. Computer program withprogram code in order to be able to implement all the steps according toclaim 1 when the program is stored on a machine readable data carrier.